Vibration Attenuation Timoshenko Beam Based on Optimal Placement Sensors/Actuators PZT Patches with LQR-MOPSO

Abstract

The main objective of this study is to reduce optimal vibration suppression of Timoshenko beam under non-periodic step and impulse inputs. Cantilever beam was modeled by Timoshenko theory and finite element numerical method. Stiffness (K), mass (M), and damping (C) matrices are extracted. Then, in order to control structure vibration, piezoelectric patches were used due to simultaneous dual behavior, i.e. switching mechanical behavior to electrical behavior (sensor) and electrical behavior to mechanical behavior (actuator). Piezoelectric patches are used in two different arrays with equal dimensions and different elements for establishing feedback control. In the following, by using quadratic optimal controller (LQR), structure vibrations became attenuated. Weighting coefficients of R and Q matrices and piezoelectric patch location have been searched by multi-objective particle swarm optimization algorithm (MOPSO). Finally, the structure underwent standard inputs of impulse and step and the results are analyzed and compared.